Gases consist of large
numbers of molecules (or atoms, in the case of the noble gases) that are in continuous,
random motion.Usually there is a
great distance between each other, so the molecules travel in straight lines
between abrupt collisions at the walls and between each other.These collisions randomize the motion of
the molecules. Most of the collisions between molecules are binary, in that
only two molecules are involved.

The volume of the molecules
of the gas is negligible compared to the total volume in which the gas is
contained.A common bond length
between atoms is about 10-10 m or 1 Angstrom. Small molecules are therefore
on the order of 10 Angstroms in diameter, or less than 10-24 Liters in
Molecular Volume, quite tiny indeed!Remember, however that there can be a great many molecules in the
sample of gas, perhaps on the order of a mole, or 6 x 1023.So that when concentrations of molecules
exceed about 1 mol/liter, then the approximation that the volume of ALL the
molecules in the container is much less than the volume of the container
itself, fails.In the case of an
ideal gas, we will assume that molecules are point masses, i.e., the volume
of a mole of gas molecules (as if they were at rest) is zero, so molecular
and container volumes never become comparable.

Attractive forces between
gas molecules are negligible.We know
that if these forces were significant, the molecules would stick
together.This happens when it rains
and gaseous water molecules stick together to form a liquid.Water vapor is a condensible gas, and this
shows us that gas molecules are sticky, but at a high enough temperature they
form only a permanent gas, because their stickiness can be considered
negligible.We will assume that in an
ideal gas, molecular attractive forces are not just small, but identically
zero.

The average kinetic energy
of the molecules does not change with time.The molecules bounce and bounce but, on average, do not slow down as
long as the temperature of the gas remains constant. Energy can be transferred
between molecules during collisions but not lost because the collisions are
perfectly elastic (not sticky)

The average kinetic energy
of the molecules is proportional to absolute temperature (A result of
Thermodynamics). At a given temperature the molecules of all species of gas,
no matter what size shape or weight, have the same average kinetic energy.

Although the molecules in a
sample of gas have an average kinetic energy (and therefore an average speed)
the individual molecules move at various speeds, i.e. they exhibit a
DISTRIBUTION of speeds; Some move fast, others relatively slowly. Collisions
change individual molecular speeds but the distribution of speeds remains the
same.

The following graph shows the
Distribution of Speeds for Gases, i.e.the fraction of the sample of gas
molecules that have a given speed is shown by the height of the curve above
the speed axis.There are no
molecules exactly at rest.

The average kinetic energy,
e, is related to the root mean square (rms) speed u

Tenaga kinetik purata, E, berhubung
dengan halaju punca kuasa dua u

Where does this number lie
on our Graph of the speed distribution?To find out, the root mean square 'average' of the distribution must
be taken (defined) in a specific way.It is defined exactly how it sounds.First your square all the speeds, then average those numbers, and take
the square root of that average.The
mean of a distribution is just the average of all the numbers in the
distribtion.The most probable value
of a distribution is also exactly what it sounds like, the speed of that the
largest fraction of molecules are travelling.In general, the mean, the root mean square and the most
probable value in a distribution are all different.

The rms speed as well as the
entire distribution of speeds of gas molecules are a function of temperature.
Below, the blue line is a cold gas and the red line is a hot gas. Note that
the rms speed, u as well as the entire speed distribution changes with
temperature for a given gas.

If, instead, we allow the
volume to change to maintain constant pressure, the volume must increase with
increasing temperature to maintain constant pressure (i.e. the number and
strength of 'hits' per wall), which is just Charles's law

Kinetic-molecular theory
states that the average kinetic energy of a mole of molecules molecules is proportional
to absolute temperature, and the proportionality constant is R, the universal
gas constant

At a given temperature, all
gases have the same average kinetic energy and for a three dimensional gas this
value is (3/2)RT. (what is the molar kinetic energy of a two dimesional gas
trapped in the surface of a metal?)